2138
J. Phys. Chem. A 1997, 101, 2138-2146
Kinetics of C2 Reactions during High-Temperature Pyrolysis of Acetylene T. Kruse and P. Roth* Institut fu¨ r Verbrennung und Gasdynamik, Gerhard-Mercator-UniVersita¨ t Duisburg, 47048 Duisburg, Germany ReceiVed: October 29, 1996; In Final Form: January 3, 1997X
The kinetics of C2 radical reactions during the first stage of acetylene high-temperature pyrolysis was studied by monitoring C, C2 and C3 radicals. Quantitative C2 detection was performed by ring dye laser absorption spectroscopy, C atoms were measured by applying atomic resonance absorption spectroscopy, and C3 radicals were monitored by their emission using a combination of a spectrograph and an intensified CCD camera system. The experiments were performed behind reflected shock waves and cover the temperature range of 2580-4650 K at pressures around 2 bar. In the first part of the study initial mixtures containing Ar with 5-50 ppm C2H2 were used. In this very low concentration range, rate coefficients for the following four k2
k1
y z C2 + H + M (R2); C2 + C2 reactions were determined: C2H2 + M S C2H + H + M (R1); C2H + M \ k3
k4
y\z C + C3 (R3); C2 + M \ y z C + C + M (R4); where k1 ) 6.96 × 1039 T-6.06 exp(-67 130/T) cm3 mol-1 -1 35 -5.16 s , k2 ) 1.74 × 10 T exp(-57 367/T) cm3 mol-1 s-1, k3 ) 3.2 × 1014 cm3 mol-1 s-1, and k4 ) 1.5 × 1016 exp(-71 650/T) cm3 mol-1 s-1. Furthermore, this experiments indicate that a modification of the JANAF1 thermodynamic data of either C, C2 or C3 seems to be necessary. In the second part, some experiments with relatively high initial acetylene concentrations up to 500 ppm C2H2 in Ar were carried out to check the validity of a more complex mechanism for the acetylene pyrolysis. Finally in a third part, a perturbation study was performed by adding 1000 ppm H2 to the initial mixtures of Ar with 20 and 50 ppm of C2H2. For k5
k6
the most important perturbation reactions, C2 + H2 y\z C2H + H (R5) and C2H + H2 y\z C2H2 + H (R6), rate coefficients of k5 ) 6.6 × 1013 exp(-4000/T) cm3 mol-1 s-1 and k6 ) 7.4 × 1014 exp(-3400/T) cm3 mol-1 s-1 were obtained.
Introduction Elementary reactions involving C2 radicals and other small carbon species like C and C3 play an important role in the hightemperature chemistry of hydrocarbons. Examples are soot formation in hot flames, diamond synthesis from gas phase pyrolysis, or the formation and decay of the recently discovered C60 fullerene.2-4 The pyrolysis of acetylene has been studied in the last decades by numerous investigators, but up to now, no quantitative measurement of C, C2, or C3 radicals has been performed. Only in one kinetic study by Beck et al.,5 C2 radicals were measured during the acetylene pyrolysis, but in this investigation C2 was monitored only by emission and thus only qualitatively. With the development of tunable and narrow bandwith CW ring dye lasers, the sensitive and quantitative detection of many di- and some triatomic molecules by direct absorption measurements became feasible. In the present study, C2 radicals were detected by ring dye laser absorption spectroscopy (RDLAS) using selected rotational transitions in the (1-0) and (0-0) bands of the C2 (d3Πg r a3Πu) Swan system. To reveal the reaction mechanism, some additional experiments were made by recording C and C3 concentrations by atomic resonance absorption spectroscopy (ARAS) and emission spectroscopy, respectively. The combination of this spectroscopic methods with the shock tube technique allowed direct observation of several C2 reactions. Experimental Section The experiments were performed behind reflected shock waves in a stainless steel shock tube of 80 mm inner diameter; see Figure 1. The tube is constructed as heatable ultrahighX
Abstract published in AdVance ACS Abstracts, February 15, 1997.
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vacuum apparatus and can be evacuated down to pressures below 5 × 10-8 mbar by a turbo-molecular pump. The shock wave is formed after bursting of aluminum diaphragms, which were 50 or 70 µm thick. Temperatures and pressures behind the reflected shock waves were calculated, on the basis of onedimensional gas dynamic equations, from the speed of the incident shock wave, which was measured by four piezoelectric pressure gauges. The gases used were carefully mixed in a stainless steel cylinder by the partial pressure method. They were of the highest commercially available purity; i.e., Ar (99.9999%), H2 (99.9999%), and C2H2 (99.6%). In a few experiments the acetylene was passed through an activated carbon filter to remove the traces of 0.4% acetone, but this experiments showed no difference from the ones with unpurified acetylene. This is in agreement with earlier studies (see, e.g., refs 6 or 7 that also showed no significant influence of acetone impurities on the kinetics of acetylene pyrolysis at low relative concentrations. The laser spectrometer (see Figure 1), used to measure the C2 concentration, consists of a CW ring dye laser from Spectra Physics, Model 380D, pumped by an Ar+ laser. To realize single-mode operation, the frequency was controlled and stabilized by a reference interferometer located in a feedback loop. For a further improvement of the detection limit, an external intensity stabilization was employed. The dye laser operates under these conditions with a line width below 500 kHz and an intensity fluctuation below 1%. The laser beam was coupled into the measurement plane of the stock tube via an optical fiber and was split into probe and reference beam prior to the shock tube. Two Si photodetectors were used in the differential technique to monitor the C2 absorption. The time absorption of about 3 µs is limited by the beam diameter and the shock speed. © 1997 American Chemical Society
Kinetics of C2 Reactions
J. Phys. Chem. A, Vol. 101, No. 11, 1997 2139
Figure 1. Experimental setup.
The C2 concentrations were measured at two different wavelengths in the d3Πg r a3Πu Swan system: (1) at λ ) 467.440 nm corresponding to the center of the three overlapping rotational lines R1(37), R2(36), and R3(35) in the (1-0) band, (2) at λ ) 516.646 nm corresponding to the band head of the (0-0) band, consisting of nine overlapping rotational lines. The line positions were taken from ref 8, and the pressure broadening was checked by scanning each line in frequency steps of 0.02 cm-1 in a series of shock-tube experiments and was found to be in agreement with ref 9. Additional measurements of C2 performed at four other lines in the (1-0) and (00) bands were in good agreement with the earlier described experiments. The oscillator strengths of the C2 Swan system, measured in the previous decades in numerous experiments, show some discrepencies. Most recent results by refs 10-12 obtained from lifetime measurements recommend a value around f00 ) 0.032, which is significantly higher than the older value of f00 ) 0.025 deduced from C2 emission behind shock waves (see, e..g., refs 13 or 14. To overcome this difficulty, we have performed oscillator-strength measurements of the C2 Swan system in some shock tube experiments; see also ref 15. The very low detection limit of less than 0.1 ppm C2, which could be achieved with the RDLAS at λ ) 516.646 nm in the (0-0) band head, allows us a direct calibration of the C2 absorption cross section and therewith determination of the oscillator strength. At very low C2H2 concentrations of 2 ppm or less and temperatures above 3500 K it can be assumed, even without a detailed knowledge of the kinetics, that the C2 formation due to two successive H atom abstractions is much faster than any subsequent C2 consumption reactions. Thus, the maximum C2 concentration must be equal to the initial C2H2 concentration. In a series of 15 shock tube experiments with initial C2H2 concentrations between 0.5 and 2 ppm an oscillator strength of f00 ) 0.037 ( 0.002 was determined, which is about 15% higher than the value obtained from the lifetime measurements. For the evaluation of the later described kinetic experiments we used our own f00 value, although the kinetic results are not significantly different when using the recent-literature value. With the knowledge of the oscillator strength together with the pressure-broadening factor, the absolute C2 concentration could directly be determined from the measured absorption by applying the LambertBeer law.
C atoms were detected at λ ) 156.1 nm by atomic resonance absorption spectroscopy (ARAS). A microwave discharge lamp, which was operated at 6 mbar in a mixture of He containing 1% CO, was used as the source for CI spectral radiation. A McPherson 0.5 m vacuum monochromator with a 100 µm slit combined with a photoelectron multiplier was used to select the respective C atom line. Since the spectral shapes of the lines emitted by the discharge lamp are not known precisely, the relation between the measured absorption and corresponding C atom concentration was obtained by calibration experiments based on thermal decomposition of CH4 at temperatures T g 3800 K. For example, an absorption of 50% corresponds to a C atom concentration of about 8 × 1012 cm-3. The time-resolved emission during C2H2 thermal decomposition in the wavelength range from 330 to 600 nm was recorded with a combination of a grid spectrograph and an intensified CCD camera. The spectral resolution was about 2 nm and the time resolution was 20 µs during a measurement time of 1 ms. A detailed description of this system is given in ref 16. Results The experiments on acetylene pyrolysis were performed with mixtures of argon containing 5-500 ppm C2H2 at temperatures 2580 K e T e 4650 K and pressures between 1.5 and 2.7 bar. In an additional series of experiments 1000 ppm H2 was added to initial mixture containing 20 or 50 ppm C2H2. The present results can be grouped in three parts: (a) experiments in mixtures containing 5-50 ppm C2H2, where C2 concentrations (RDLAS), C concentrations (ARAS), and C3 concentrations (CCD) were measured, (b) experiments in mixtures containing 100-500 ppm C2H2, where only C2 was measured, and (c) perturbation experiments in mixtures of argon with 20 or 50 ppm C2H2, where the formation of C2 was perturbed by the addition of 1000 ppm H2 to the initial mixture. Typical C2 concentration profiles belonging to the first group of experiments are shown in Figure 2 for three different temperatures and an initial C2H2 concentration of 50 ppm diluted in Ar. The directly measured ring dye laser absorption profiles were converted via the Lambert-Beer law into concentrations based on f00 ) 0.037. The noisy drawn lines belong to the experiments, and the dotted lines represent computer simulations, which will be discussed later. After a fast rise, all profiles
2140 J. Phys. Chem. A, Vol. 101, No. 11, 1997
Figure 2. Measured and calculated C2 concentration profiles at three different temperatures obtained during pyrolysis of 50 ppm C2H2 diluted in Ar.
Figure 3. Emission spectrum of C2 and C3 during acetylene pyrolysis at a reaction time of 200 µs. Initial mixture: 10 ppm C2H2 diluted in Ar.
drop rapidly to about 85% of the peak concentration. In the two experiments with temperatures below 4000 K, and C2 concentration reaches a nearly constant level after the initial peak, whereas the signal of the T ) 4450 K experiment shows a further decrease within the observation time. To clarify the origin of the initial peak in the C2 absorption, additional experiments with ARAS and the CCD camera were performed. Figure 3 shows an emission spectrum obtained during the thermal decomposition of 10 ppm acetylene in argon at T ) 3450 K. It was recorded at a reaction time of 200 µs. Two main features are of importance: the strong emission of the C2(d3Πg r a3Πu) Swan bands at λ > 430 nm and the weak emission of the C3(A1Πu r X1Σ+ g ) bands in the spectral range 360 nm < λ < 420 nm.17 These emission spectra can be evaluated in order to get quantitative C3 concentration profiles. For this purpose, the emission signals (λ) of the ∆V ) 0 progressions of C2 and the A1Πu r X1Σ+ g transition of C3 were integrated with respect to the wavelength at a fixed time τ for each experiment. The integrated emission intensities IC(τ)2 and IC(τ)3 at a fixed time τ were defined as
IC(τ)2 )
∫480522nmnm (τ)(λ) dλ
IC(τ)3 )
∫350420nmnm (τ)(λ) dλ
with (τ)(λ) being the wavelength dependent emission at t ) τ. With the knowledge of the simultaneously measured C2
Kruse and Roth
Figure 4. Measured and calculated C, C2, and C3 concentrations during pyrolysis of 10 ppm acetylene diluted in Ar.
Figure 5. C2 concentration profiles obtained from experiments with different initial C2H2 concentrations at temperatures around 3500 K and pressures of about 2 bar, in comparison with computer simulation.
concentration by the RDLAS, the C3 concentration can be calibrated at the time τ by
IC(τ)3
[C3](τ)
fel,C3 νC3 3 exp(-hcνC3/kT)
) IC(τ)2
[C2](τ)
3 ∑i fii,C νii,C 2
2
exp(-hcνii,C2/kT)
whereby the sum must be taken over the progression of the C2 bands, and νC3 and νii,C2 are the respective mean band wavenumbers of C3 and C2. The electronic oscillator strength fel,C3 was taken from ref 18 and fii,C2 was calculated from the measured f00 oscillator strength of C2 using the Franck-Condon factors qii,C2 given in ref 19. After calibration of the C3 emission against C3 concentration at one fixed time τ, the proportionality factor between emission and concentration of C3 is known for the whole time scale of this specific shock tube experiment. A typical result of a C3 concentration profile obtained from an emission signal is shown in Figure 4 together with a C2 profile and a C atom concentration profile (see open circles) obtained by ARAS. The experimental conditions are 10 ppm C2H2, T ) 3450 K, and p ) 2.2 bar. The decrease in the C2 concentration at early reaction time is accompanied by an increase in C3 and C atom concentration. At later reaction times, the concentration of all three species reach a nearly constant level. The computer simulation shown in Figure 4 as dotted lines will be discussed later.
Kinetics of C2 Reactions
J. Phys. Chem. A, Vol. 101, No. 11, 1997 2141 The results of Figure 4 also clearly indicate a strong formation of both C and C3 during the time of about 100 µs, when the initial C2 peak decreases to a nearly constant concentration level. It seems quite obvious to interpret this behavior by the bimolecular reaction: 3
C2 + C2 h C + C3
(R3)
Furthermore, the observed additional decrease in the C2 concentration at temperatures T > 4000 K during the whole observation time of 700 µs (see Figure 2) suggests a dissociation of C2: 4
C2 + M h C + C + M Figure 6. Measured and calculated C2 concentration profiles at four different temperatures obtained from the pyrolysis of 20 ppm C2H2 diluted in Ar perturbated by the addition of 1000 ppm H2.
The second group of pyrolysis experiments was performed in mixtures containing 100-500 ppm C2H2 diluted in Ar. The reason for chosing this higher initial concentrations was to verify existing kinetic models for C2H2 pyrolysis by comparing calculated C2 profiles with measured ones. Three typical measured C2 profiles from a total of about 10 experiments are shown in Figure 6; see noisy lines. At time t ≈ 0 C2 increases very rapidly, but different from the low C2H2 concentration experiments, the initial C2 peak structure diminishes with increasing initial C2H2 concentration nearly completely. Furthermore, a second slower C2 increase appears, which reaches a flat maximum or a constant level after some 100 µs. The result of all experiments together with the experimental conditions are summarized in Table 1. The last group of experiments includes perturbation of C2H2 pyrolysis by H2. Four examples of measured C2 profiles in mixtures of Ar with 20 ppm C2H2 and 1000 ppm H2 are shown in Figure 6. The peaks at t ) 0 and t < 0 are schlieren signals caused by the incident and reflected shock wave when passing through the laser beam. The structure of the C2 signals is very different from those of the H2-free mixtures. A direct comparison of measured C2 profiles obtained at identical temperatures of T ) 3380 K from a mixture of 20 ppm C2H2 diluted in argon with Figure 6) and without (Figure 7) addition of H2 clearly illustrates this effect. As a result of the H2 addition, the initial rapid increase in the C2 formation (see Figure 7) is very moderate in Figure 6 and the initial peak at t ≈ 40 µs disappears completely. Also the maximum amount of C2 formed is different in Figures 6 and 7 by a factor of 1.8. In general the H2 addition attenuates the C2 formation during pyrolysis of C2H2. The results of all experiments together with the experimental conditions are also summarized in Table 1. Discussion It seems useful to discuss the experimental observations during pyrolysis of C2H2 within the meaning of the three groups of experiments introduced earlier. The very rapid formation of C2 during high-temperature pyrolysis of acetylene at low relative C2H2 concentrations (group I experiments), as shown in Figures 2 and 4, can kinetically be understood by a successive abstraction of H atoms: 1
C2H2 + M h C2H + H + M 2
C2H + M h C2 + H + M
(R1) (R2)
(R4)
For the computer simulation of the measured C2 time histories, this simple mechanism was extended by additional reactions listed in Table 2, which have, however, only a very minor influence for initial C2H2 concentrations of 50 ppm or less. A problem is that the experimentally observed steady state C2 concentration at later reaction times (see Figures 2 and 4) is significantly higher than the calculated value. An example is given in Figure 7. The dotted line represents the calculated C2 concentration, which is for times t > 100 µs significantly below the measured steady state value. This is due to the JANAF thermodynamic data1 for C, C2, and C3, which are equal to those given in ref 20. For the example given in Figure 7 these literature data yield an equilibrium constant of Kc,3 ) 10. The best fit to the experiments however can be obtained with an equilibrium constant of Kc,3 ) 1.9, which increases the importance of the backward reaction R3; see Figure 7. This can be achieved by either increasing the Gibbs free energies of C or C3 by 11 kcal or by decreasing the value of C2 by 5.5 kcal or by a combination of both. A change in the Gibbs free energy can be obtained either by a change in the enthalpies or the entropies of the species. Since the necessary variation in ∆G° is constant over the studied temperature range between 2580 and 4650 K, it seems near at hand to attribute it to changes in the enthalpies rather than in the entropies of the species. Recently Urdahl et al.21 determined experimentally a value for the heat of formation of C2, which is by about 4 kcal/mol lower than the JANAF value. A lower value was also recommended in a theoretical study.22 Therefore and for reasons discussed later, we think that a reduction of the JANAF value1 for the enthalpy of C2 by about (5.5 ( 0.5) kcal mol-1 corresponding to a change in the heat of formation from ∆fH0298.15 ) 200.2 kcal mol-1 to ∆fH0298.15 ) 194.7 kcal mol-1 is most likely to fullfill the requirements of the equilibrium constant of reaction R3. With the above mechanism and the modification in the thermodynamic data of C2, it is possible to fit the measured C2 profiles. It is clear that the rapid initial C2 increase is mainly sensitive to reactions R1 and R2. A value for the rate coefficient k1 is given by ref 23 for the temperature range 1850 K e T e 3500 K on the basis of experiments of Frank and Just.6 In a first attempt we used this rate coefficient and modified only k2 to fit the initial C2 increase. As indicated in Figure 8 the initial C2 increase could not be fitted satisfactorly, especially for temperatures below 3200 K. Moreover, the resulting rate coefficient k2 necessary to fit the further parts of the C2 profiles showed an extraordinary small activation energy around 67 kcal, which is only 57% of the reaction enthalpy for R2. We therefore started to fit the measured C2 profiles by varying both rate coefficients k1 and k2 of the above mechanism. This results in nearly perfect fits of the experimental traces, even for the colder experiments; see Figure 8. The resulting rate coefficients k1
2142 J. Phys. Chem. A, Vol. 101, No. 11, 1997
Kruse and Roth
TABLE 1: Experimental Conditions and Characteristics of Measured C2 Concentration Profiles Obtained during High-Temperature Pyrolysis of Acetylene Highly Diluted in Ar T (K)
p (bar)
[C2H2]0 (ppm)
tpeak (µs)
[C2]peak (cm-3)
[C2]100µs (cm-3)
[C2]300µs (cm-3)
[C2]600µs (cm-3)
3082 3225 3431 3501 3552 3610 2580 2580 2580 2626 2685 2775 2824 2850 2866 3018 3053 3062 3113 3150 3281 3293 3345 3365 3450 3523 3652 3773 3830 4061 4155 4380 4575 3382 3558 3734 2945 2999 3175 3483 3650 3745 3808 3931 3976 3990 4085 4189 4280 4403 4437 4450 4518 4609 4634 3489 3572 3510 3509 3430 3360 3250 3490 3605 3785
2.24 2.15 2.05 2.27 2.16 2.09 2.45 2.45 2.45 2.51 2.27 2.49 2.41 2.12 2.35 2.12 2.31 2.40 2.40 2.06 1.95 1.99 2.40 2.17 2.20 2.02 2.09 2.02 1.98 0.76 1.92 1.80 0.75 2.18 2.15 1.98 2.14 2.23 2.23 2.11 1.92 1.97 2.01 2.09 2.04 1.98 1.98 1.89 1.85 1.83 1.83 1.82 1.71 1.60 1.58 2.10 2.17 2.14 2.12 2.21 2.01 2.06 2.13 1.90 1.83
5. 5 5 5 5 5 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 20 20 20 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 75 100 125 150 200 250 500 500 500 500
155 105 61 49 43 40 540 520 520 490 450 305 235 225 250 150 100 130 113 105 80 73 55 57 40 40 31 26 23 30 14 10 18 45 30 23 121 118 63 32 22 18 16 12 12 11 16 11 10 9 9 9 9 7 6 26 22 22 22 22 24 40 18 13 11
6.2 × 1012 8.2 × 1012 1.0 × 1013 1.1 × 1013 1.2 × 1013 1.3 × 1013 2.3 × 1012 2.5 × 1012 2.5 × 1012 2.8 × 1012 2.9 × 1012 5.2 × 1012 5.8 × 1012 5.4 × 1012 4.9 × 1012 6.8 × 1012 1.1 × 1013 8.5 × 1012 9.6 × 1012 9.0 × 1012 1.1 × 1013 1.3 × 1013 1.6 × 1013 1.5 × 1013 1.9 × 1013 1.8 × 1013 2.1 × 1013 2.2 × 1013 2.2 × 1013 9.2 × 1012 2.4 × 1013 2.5 × 1013 9.3 × 1012 2.1 × 1013 2.8 × 1013 3.2 × 1013 1.7 × 1013 1.7 × 1013 2.4 × 1013 3.8 × 1013 4.6 × 1013 5.2 × 1013 5.8 × 1013 6.8 × 1013 6.8 × 1013 6.9 × 1013 7.3 × 1013 7.5 × 1013 7.7 × 1013 7.3 × 1013 7.4 × 1013 7.2 × 1013 7.8 × 1013 7.4 × 1013 7.2 × 1013 4.6 × 1013 6.2 × 1013 6.3 × 1013 6.3 × 1013 7.9 × 1013 9.1 × 1013 1.2 × 1014 1.5 × 1014 1.6 × 1014 1.7 × 1014
5.4 × 1012 8.2 × 1012 8.5 × 1012 7.8 × 1012 8.0 × 1012 9.5 × 1012 1.5 × 1011 2.0 × 1011 2.0 × 1011 2.0 × 1011 4.5 × 1011 2.2 × 1012 3.0 × 1012 2.8 × 1012 2.5 × 1012 6.2 × 1012 1.1 × 1013 7.9 × 1012 9.5 × 1012 9.0 × 1012 1.1 × 1013 1.1 × 1013 1.3 × 1013 1.2 × 1013 1.4 × 1013 1.2 × 1013 1.3 × 1013 1.3 × 1013 1.2 × 1013 6.8 × 1012 1.3 × 1013 1.1 × 1013 5.1 × 1012 1.6 × 1013 1.8 × 1013 1.9 × 1013 1.6 × 1013 1.5 × 1013 2.1 × 1013 2.9 × 1013 3.7 × 1013 4.0 × 1013 4.4 × 1013 4.5 × 1013 4.5 × 1013 4.7 × 1013 5.8 × 1013 5.8 × 1013 5.5 × 1013 5.0 × 1013 4.8 × 1013 4.9 × 1013 4.0 × 1013 3.5 × 1013 3.0 × 1013 3.9 × 1013 5.0 × 1013 6.2 × 1013 6.1 × 1013 8.8 × 1013 9.5 × 1013 1.6 × 1014 2.5 × 1014 2.4 × 1014 3.2 × 1014
4.8 × 1012 4.7 × 1012 4.5 × 1012 5.2 × 1012 5.7 × 1012 6.0 × 1012 1.3 × 1011 1.4 × 1012 1.4 × 1012 1.8 × 1012 2.3 × 1012 5.1 × 1012 5.4 × 1012 5.0 × 1012 4.8 × 1012 5.5 × 1012 6.2 × 1012 6.1 × 1012 6.4 × 1012 6.0 × 1012 6.5 × 1012 6.7 × 1012 8.4 × 1012 8.3 × 1012 1.4 × 1013 8.2 × 1012 1.2 × 1012 1.2 × 1013 1.3 × 1013 5.0 × 1012 1.2 × 1013 5.0 × 1012 2.7 × 1012 1.3 × 1013 1.7 × 1013 2.1 × 1013 1.1 × 1013 1.2 × 1013 1.6 × 1013 3.2 × 1013 4.2 × 1013 4.5 × 1013 4.7 × 1013 4.7 × 1013 4.6 × 1013 4.9 × 1013 4.9 × 1013 4.0 × 1013 3.2 × 1013 1.9 × 1013 1.6 × 1013 1.7 × 1013 8.0 × 1012 3.0 × 1012 2.0 × 1012 4.9 × 1013 6.3 × 1013 7.9 × 1013 7.3 × 1013 1.1 × 1014 1.3 × 1014 2.0 × 1014 2.8 × 1014 2.5 × 1014 3.7 × 1014
3.0 × 1012 4.0 × 1012 4.2 × 1012 5.0 × 1012 5.5 × 1012 5.9 × 1012 2.2 × 1012 2.4 × 1012 2.4 × 1012 2.5 × 1012 2.5 × 1012 4.1 × 1012 3.9 × 1012 3.8 × 1012 3.7 × 1012 4.0 × 1012 5.2 × 1012 4.9 × 1012 5.6 × 1012 5.1 × 1012 6.1 × 1012 6.3 × 1012 8.4 × 1012 8.4 × 1012 1.4 × 1013 9.0 × 1012 1.2 × 1012 1.2 × 1013 1.2 × 1013 4.8 × 1012 8.5 × 1012 1.2 × 1012 8.0 × 1011 1.3 × 1013 1.7 × 1013 2.2 × 1013 1.0 × 1013 1.2 × 1013 1.6 × 1013 3.5 × 1013 4.2 × 1013 4.3 × 1013 4.8 × 1013 4.8 × 1013 4.2 × 1013 4.0 × 1013 3.0 × 1013 1.6 × 1013 1.0 × 1013 3.1 × 1012 2.5 × 1012 2.7 × 1012 1.0 × 1012 5 × 1011 2 × 1011 5.1 × 1013 6.3 × 1013 8.5 × 1013 8.7 × 1013 1.2 × 1014 1.5 × 1014 2.2q × 1014 2.7 × 1014 2.6 × 1014 3.4 × 1014
T (K) 2890 3380 3550 3830 3990 3128 3378 3440 3440 3700 3810
p (bar) 2.13 2.22 1.85 1.91 1.82 2.23 2.19 1.97 1.97 1.95 1.83
[C2H2]0 (ppm) 20 20 20 20 20 50 50 50 50 50 50
[H2]0 (ppm) 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000
tpeak (µs)
[C2]peak (cm-3)
[C2]100µs (cm-3)
[C2]300µs (cm-3)
[C2]600µs (cm-3)
1.0 × 10 3.2 × 1012 6.3 × 1012 1.4 × 1013 1.8 × 1013 1.9 × 1012 6.3 × 1012 9.5 × 1012 9.5 × 1012 1.8 × 1013 2.0 × 1013
2.0 × 8.1 × 1012 1.3 × 1013 1.5 × 1013 7.2 × 1012 6.9 × 1012 1.7 × 1013 2.0 × 1013 2.0 × 1013 2.5 × 1013 1.6 × 1013
7.0 × 1011 1.2 × 1013 1.1 × 1013 5.1 × 1012 1.5 × 1012 1.3 × 1013 2.7 × 1013 2.7 × 1013 2.7 × 1013 1.2 × 1013 4.0 × 1012
11
395 195 110
1.3 × 1013 1.6 × 1013 1.8 × 1013
260 150
2.6 × 1013 2.3 × 1013
1011
Kinetics of C2 Reactions
J. Phys. Chem. A, Vol. 101, No. 11, 1997 2143 TABLE 2: Simplified Reaction Mechanism for the High-Temperature Pyrolysis of Acetylenea reaction
Figure 7. Simulation of C2 concentration profiles with original and modified thermodynamic data for an experiment with 20 ppm C2H2 diluted in Ar.
and k2 obtained from a total of 38 experiments are summarized in Figures 9 and 10. The points for k1 show a weak nonArrhenius behavior, which can in the lower temperature regime be represented by an activation energy of about 104 kcal mol-1. For the whole temperature range 2580 K e T e 3830 K a good fit to the experiments is possible by the modified Arrhenius expression:
k1 ) 6.96 × 1039 T-6.06 exp(-67 130/T) cm3 mol-1 s-1 Our results for k1 at 3000 K is by a factor of 2 higher than the value of Frank and Just.6 The data points for the rate coefficient k2, summarized in Figure 10, can be represented by the Arrhenius expression:
k2 ) 1.1 × 1015 exp(-41 868/T) cm3 mol-1 s-1 The relatively low activation energy of 83 kcal favors the suggested reduction in the heat of formation for C2. A modified Arrhenius expression similar to that of k1 based on the heat of reaction for reaction R2 of 114 kcal mol-1 would result in a temperature exponent of -5.16. The rate coefficients of the bimolecular reaction R3 and the thermal decomposition reaction R4 were also determined by computer fittings from the measured C2 concentration profiles. Individual results obtained are summarized in Figures 11 and 12. They can be represented by the Arrhenius expressions:
k3 ) (3.2 ( 0.4) × 1014 cm3 mol-1 s-1 k4 ) (1.5 ( 0.5) × 1016 exp(-71 660/T) cm3 mol-1 s-1 The rate coefficient k3 was found to be independent of temperature. The activation energy of reaction R4 of 142 ( 5 kcal mol-1 is in good agreement with published values for the C2 bond dissociation energy; see, e.g., refs 21 and 24-27, and the values resulting from the thermodynamic data of C and C2. All computer simulations for obtaining the given rate coefficients k1-k4 were performed both with the reaction mechanism R1R4 and with the more extended mechanism listed in Table 2. The results were nearly the same. The interpretation of the group II experiments with higher initial C2H2 concentrations of 100-500 ppm (see examples in Figure 6) needs an extension of the thermal decomposition mechanism. We started with a system of 145 elementary reactions, mainly taken from Kiefer et al., refs 28 and 29. By careful sensitivity analysis, the 60 reactions listed in Table 2
C2H2 + M h C2H + H + M C2H + M h C2 + H + M C2 + C2 h C3 + C C2 + M h C + C + M C2 + H2 h C2H + H C2H + H2 h C2H2 + H C4 f 4C(s) C + CH h C2 + H C + C2H h C3 + H C + C2H2 h C3H + H C2 + CH h C3 + H C2 + C2H h C4 + H C2 + C2H2 h C4H + H C2 + C4H h C2H + C4 C2 + C4H h C6 + H C2 + C4H2 h C6H + H C2 + C6H h C2H + C6 C4 + C2H h C6 + H C4 + C6 H h C4H + C6 CH + H h C + H2 CH + CH h C2 + H + H CH2 + H h CH + H2 C2H + C2H h C2H2 + C2 C2H + C2H h C4H + H C2H + C2H2 h C4H2 + H C2H + C4H2 h C4H + C2H2 C2H + C4H2 h C6H2 + H C2H + C6H h C6 + C2H2 C2H + C6H h C2 + C6H2 C2H2 + C2H2 h C4H2 + H2 C2H2 + C2H2 h C4H3 + H C2H2 + C4H h C6H2 + H C2H2 + C6H h C8H2 + H C3H + H h C3 + H2 C3H2 + H h C3H + H2 C4H + H h C4 + H2 C4H + H2 h C4H2 + H C4H + C4H h C4 + C4H2 C4H + C4H2 h C8H2 + H C4H + C6H h C4 + C6H2 C4H + C6H h C4H2 + C6 C4H + C6H2 h C4H2 + C6H C4H + C8H h C4 + C8H2 C6H + H h C4 + C2H2 C6H + H h C6 + H2 C6H + H2 h C6H2 + H C6H + C6H h C6H2 + C6 C6H2 h C6H + H H + C4 + M h C4H + M C4H2 h C4H + H C3 + M h C2 + C + M C2 + C2 + M h C4 + M CH + M h C + H + M CH2 + M h C + H2 + M CH2 + M h CH + H + M CH3 + M h CH2 + H + M C3H + M h C3 + H + M C3H2 + M h C3H + H + M C2 + C4H + M h C6H + M H2 + M h H + H
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 a
A/cm3 mol-1 s-1
n
6.96 × 1039 1.74 × 1035 3.20 × 1014 1.50 × 1016 6.60 × 1013 7.40 × 1014 8.00 × 103 5.00 × 1014 7.00 × 1014 4.00 × 1014 2.00 × 1014 1.20 × 1014 1.00 × 1014 1.20 × 1014 1.20 × 1014 1.20 × 1014 1.20 × 1014 1.20 × 1014 1.20 × 1014 1.10 × 1014 1.00 × 1014 1.10 × 1014 1.00 × 1013 1.00 × 1014 5.00 × 1014 1.00 × 1013 1.20 × 1014 1.00 × 1013 1.20 × 1014 1.50 × 1013 1.50 × 1014 1.20 × 1014 1.20 × 1014 1.00 × 1014 6.31 × 1013 2.00 × 1013 4.07 × 105 1.20 × 1014 1.20 × 1014 1.20 × 1014 1.00 × 1013 1.00 × 1013 1.00 × 1013 1.00 × 1014 2.00 × 1013 4.07 × 105 1.00 × 1013 6.00 × 1013 1.74 × 1037 1.30 × 108 4.00 × 1016 1.00 × 1027 1.90 × 1014 1.15 × 1014 2.88 × 1014 1.58 × 1015 1.58 × 1014 1.00 × 1015 2.09 × 1023 2.23 × 1014
-6.06 -5.16 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 2.4 0. 0. 0. 0. 0. 0. 0. 0. 2.4 0. 0. -5.5 2.2 0. -3.0 0. 0. 0. 0. 0. 0. -3.0 0.
EA/ (cal/mol) ref 133 400. 114 000. 0. 142 400. 8 000. 6 700. 0. 0. 0. 12 000. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 42 700. 56 000. 0. 0. 0. 0. 0. 200. 0. 0. 0. 0. 0. 0. 0. 0. 200. 0. 0. 0. 122 600. 150 000. 0. 66 968. 55 820. 79 030. 76 610. 39 420. 60 000. 0. 96 080.
s.t. s.t. s.t. s.t. s.t. s.t. s.t. est. est. 29 29 28 28 28 28 28 28 28 28 29 29 29 28 28 est. 28 28 28 28 28 28 28 28 29 29 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 29 28 35 29 29 29 29 29 28 34
Rate coefficient k ) ATn exp(-EA/RT).
were found to have influence on the measured C2 profiles. Reactions R1-R4 are identical to those discussed earlier, and the rate coefficients of R5 and R6 will be discussed later. It was found that the second, slower C2 increase observed in Figure 5 is mainly sensitive to the reactions R12, R52, R19, R36, and R14 involving the species C2, C2H, C4, C4H, C6, and C6H. Since many of the sensitive reactions have equilibrium constants close to 1, the thermodynamic properties, i.e., the Gibbs free energies, of this species become very important for these experimental conditions. The thermodynamic properties at 3500 K of some
2144 J. Phys. Chem. A, Vol. 101, No. 11, 1997
Figure 8. Measured and calculated C2 concentration profile obtained at relatively low temperature. The dotted line shows the best simulation using the literature value for k1 varying only k2. The dashed lines shows the best simulation fitting obtained by varying both k1 and k2.
Kruse and Roth
Figure 11. Rate coefficient of the reaction C2 + C2 h C + C3.
Figure 12. Rate coefficient of the reaction C2 + Ar h C + C + M.
Figure 9. Rate coefficient of the reaction C2H2 + M h C2H + H + M. The dotted line corresponds to the Arrhenius expression and the solid line to a modified Arrhenius expression (see text).
Figure 10. Rate coefficient of the reaction C2H + M h C2 + H + M. Dotted line, Arrhenius expression; solid line, modified Arrhenius expression.
important species used for our kinetic modeling are shown in Table 3. Again a satisfactory fit of the measured C2 profiles could only be obtained with the earlier suggested change in the thermodynamics of C2. An additional modification of the thermodynamic properties of C4 was also suitable. The best fit was achieved by reducing the Gibbs free energy of C4 by about 20 kcal mol-1 compared to the value given by Burcat.30
TABLE 3: Thermodynamic Data at Room Temperature and 3500 K of Some Important Species Used for the Kinetic Modeling species
S°298.15 (cal/mol/K)
S°3500 (cal/mol/K)
H°298.15 (kcal/mol)
H°3500 (kcal/mol)
ref
H C C2 C2H C2H2 C3 C3H C4 C4H C6 C6H
27.4 37.8 47.6 49.6 48.0 56.7 54.2 60.4 63.5 57.9 74.1
39.6 50.1 70.1 79.7 88.2 83.2 91.8 111.8 117.8 113.2 154.1
52.1 171.3 194.7 135.0 54.2 196.0 163.5 247.1 192.0 282.2 213.2
68.0 187.5 224.4 178.4 113.0 233.5 219.6 311.7 268.6 360.7 326.6
20 20, 1 s.t. 20 20 20, 1 30 s.t. 30 30 20
This can be achieved, e.g., by increasing the entropy of C4 by 5.7 cal mol-1 K-1 or 6% compared to the value given by Burcat.30 The possibility of a too low literature value of the C4 entropy was already discussed by Kiefer et al.28 on the basis of experiments performed by Heath et al.31 An example illustrating the different effects is shown in Figure 13. The experimental conditions are T ) 3492 K, p ) 2.14 bar, and 500 ppm C2H2 diluted in Ar. The noisy line comes from the experiment, the dotted line represents a calculation with the Burcat value for the entropy of C4, and the dashed line was calculated with the modified C4 data. A nearly perfect agreement, see the dashed dotted line, with the experimental profile even at later reaction time was achieved by assuming the formation of solid carbon. Following the suggestion of Kiefer et al.,32 reaction R7 was introduced which converts in an irreversible way C4 into solid carbon. Similar good agreement
Kinetics of C2 Reactions
J. Phys. Chem. A, Vol. 101, No. 11, 1997 2145
Figure 13. Comparison of different models used to describe the measured C2 concentration for an experiment 500 ppm C2H2 diluted in Ar, T ) 3490 K and p ) 21.4 bar.
Figure 15. Rate coefficient of the reaction C2 + H2 h C2H + H.
Figure 16. Rate coefficient of the reaction C2H + H2 h C2H2 + H.
the Figures 15 and 16. The points can be approximated by the Arrhenius expressions: Figure 14. (upper) Measured and calculated C2 profiles during the pyrolysis of 50 ppm C2H2 diluted in Ar enriched with 1000 ppm H2. (lower) Normalized sensitivity coefficients of the H2 perturbation reactions R5 and R6 describing the influence on the C2 concentration for this experiment.
was also obtained for the other experiments; see Figure 6, dashed lines. The best fit rate coefficient used during the computer simulation was k7 ) (8 ( 3) × 103 s-1. The last group of results includes five experiments of 20 ppm C2H2 diluted in Ar and five experiments of 50 ppm C2H2 diluted in Ar enriched with 1000 ppm H2. We again started our computer simulation on the basis of the complete mechanism consisting of 145 reactions. It is obvious that now reactions R5 and R6 k5
C2 + H2 y\z C2H + H k6
C2H + H2 y\z C2H2 + H
(R5) (R6)
have a high sensitivity to the C2 concentration. As can be seen in Figure 14, both reactions are responsible for the drastic slowdown of the C2 rise, whereby reaction R6 is most sensitive in the first 50 µs and reaction R5 in the following 200 µs. Thus, both rate coefficients can be evaluated seperately on the basis of computer fittings of the experimental C2 concentrations by varying the rate coefficients k5 and k6. Individual results obtained from fittings at early reaction time are summarized in
k5 ) 6.6 × 1013 exp(-4000/T) cm3 mol-1 s-1 k6 ) 7.4 × 1014 exp(-3400/T) cm3 mol-1 s-1 The rate coefficient k5 has not been measured before in the hightemperature regime, but the value is in accordance with an estimation by Kiefer et al.28 Our value for k6 is at 3000 K by factor of 20 higher than the value recomended by Baulch et al.33 An estimated value by Kiefer et al.28 and a value obtained from the backward reaction of R6 measured by Frank and Just6 are relatively close to our value. The nearly perfect agreement of the simulations with the experimental profiles (see Figure 5) for the whole measurement time of 1000 µs could only be obtained by including the complete mechanism of Table 2. The slow disappearance of the C2 at later reaction times in the higher temperature experiments is mainly due to reactions involving H, C, C2, and CH as, for example reactions, R8, R9, and R53. The rate coefficients of this three reactions and the rate coefficients of reactions R12 and R25 were adjusted in a range of (30% compared to the values given in Table 2 to obtain best agreement between experiment and simulation. For the H2 dissociation, which is also very sensitive to the C2 profiles at later reaction time, the rate coefficient recommended by Baulch et al.34 was used. Again, the thermodynamic properties of the species listed in Table 3 proved to be very important, and we found that the best fit was again possible with the above suggested changes in the thermodynamics of C2 and C4.
2146 J. Phys. Chem. A, Vol. 101, No. 11, 1997 Conclusion C2 measurements during high-temperature pyrolysis of acetylene diluted in Ar covering the temperature range of 25804650 K could be verified in a wide range of mixture compositions by a consistent mechanism of 60 reactions. In the very low concentration range of 50 ppm C2H2 or less, a simplified description of the measured C2 profiles could be given on the basis of four elementary reactions, for which rate coefficients were evaluated. A discrepancy in the JANAF thermodynamic data1 of either C, C2, or C3 was revealed and tentatively explained by a reduction of the JANAF ∆fH0298.15 value for C2 by about 5.5 kcal/mol. In a series of experiments with higher C2H2 concentrations up to 500 ppm, a complex mechanism of 145 reactions was checked and reduced by sensitivity analysis to 60 elementary reactions. The simulation of the experiments showed a high sensitivity to the thermodynamic properties of the involved species, especially C2, and C4. With slight modification in the thermodynamic properties of this species and an assumed conversion of C4 into solid carbon, the measured C2 concentration profiles could nearly perfectly be fitted. In a perturbation study with addition of H2, rate coefficients for the reactions C2 + H2 h C2H + H and C2H + H2 h C2H2 + H could be determined. In general we found that an accurate knowledge of the thermodynamic data of the involved species is crucial for a correct description of the acetylene pyrolysis. Acknowledgment. The authors thank Mrs. C. Kmiecik, Mrs. N. Schlo¨sser, and Mr. L. Jerig for their help in conducting the experiments. We also thank Prof. Th. Just, DLR Stuttgart, for helpful discussion. The financial support of the Deutsche Forschungsgemeinschaft is gratefully acknowledged. References and Notes (1) Chase, M. W., Jr.; Davies, C. A.; Downey, J. R.; Frurip, D. J.; McDonald, R. A.; Syverud, A. N. JANAF thermochemical tables. J. Phys. Chem. Ref 1985, 14. (2) Gaydon, A. G.; Wolfhard, H. G. Flames; Chapman and Hall, New York, 1979. (3) Perry, M. D.; Raff, L. M. J. Phys. Chem. 1994, 98, 4375-4381. (4) O’Brien, S. C.; Heath, J. R.; Curl, R. F.; Smalley, R. E. J. Chem. Phys. 1988, 88, 220-230. (5) Beck, W. H.; Mackie, J. C. J. Chem. Soc., Faraday Trans. 1975, 71, 1363-1371. (6) Frank, P.; Just, T. Combust. Flame 1980, 38, 231-248. (7) Kern, R. D.; Xie, K.; Chen, H.; Kiefer, K. J. H. High Temperature Pyrolysis of Acetylene and Diacetylene Behind Reflected Shock Waves. 23th Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, 1990; pp 69-75.
Kruse and Roth (8) Phillips, J. G.; Davis, S. P. The Swan System of The C2 Molecule, Berkeley Analysis of Molecular Spectra; University of California Press: Berkeley, Los Angeles, 1984. (9) Sviridov, A. G.; Sobolev, N. N.; Novgorodev, M. Z.; Arytyunova, G. A. J. Quant. Spectrosc. Radiat. Transfer 1966, 6, 875-892. (10) Naulin, C.; Costes, M.; Dorthe, G. Chem. Phys. Lett. 1988, 143, 496-500. (11) Bauer, W.; Bielefeld, M.; Becker, K. H.; Meuser, R. Chem. Phys. Lett. 1986, 123, (1,2), 33-36. (12) Stark, G.; Davis, S. P. Z. Phys. A: At. Nucl. 1985, 321, 75-77. (13) Arnold, J. O. J. Quant. Spectrosc. Radiat. Transfer 1968, 8, 17811794. (14) Cooper, D. M.; Nicholls, R. W. J. Quant. Spectrosc. Radiat. Transfer 1975, 15, 139-150. (15) Kruse, T.; Roth, P. To be published. (16) Von Gersum, S.; Kruse, T.; Roth, P. Ber. Bunsen-Ges. Phys. Chem. 1994, 98, 979-982. (17) Kiess, N. H.; Broida, H. P. Can. J. Phys. 1956, 34, 1471-1479. (18) Becker, K. H.; Tatarczyck, T. Chem. Phys. Lett. 1979, 60, 502506. (19) Danylewych, L. L.; Nicholls, R. W. Proc. R. Soc. London A 1974, 339, 197-222. (20) Kee, R. J.; Rupley, F. M.; Miller, J. A. The CHEMKIN Thermodynamic Data Base. SANDIA REPORT, SAND95-8215; Sandia National Laboratories: Albuquerque, NM, 1995. (21) Urdahl, R. S.; Jackson, W. M.; Bao, Y.; Chem. Phys. Lett. 1991, 178, 425-428. (22) Bauschlicher, C. W., Jr.; Langhoff, S. R. Chem. Phys. Lett. 1990, 173, 367-370. (23) Warnatz, J. Rate Coefficients in the C/H/O-System. In Combustion Chemistry; Gardiner, W. C., Jr., Ed.; Springer-Verlag: New York, 1984. (24) Ervin, K. M.; Gronert, S.; Barlow, S. E.; Gilles, M. K.; Harrision, A. G.; Bierbaum, V. M.; Ellison, G. B. J. Am. Chem. Soc. 1990, 112, 5750. (25) Bauschlicher, C. W., Jr.; Langhoff, S. R. Astrophy. J. 1988, 332, 531. (26) Kordis, J.; Gingerich, K. A. J. Chem. Phys. 1973, 58, 5058. (27) Gaydon, A. G.; Wolfhard, H. G. Dissociation Energies and Spectra of Diatomic Molecules; Chapman and Hall: London, 1968. (28) Kiefer, J. H.; Sidhu, S. S.; Kern, R. D.; Xie, K.; Chen, H.; Harding, L. B. Combust. Sci. Technol. 1992, 82, 101-130. (29) Kiefer, J. H.; Kumaran, S. S. J. Phys. Chem. 1993, 97, 414-420. (30) Burcat, A.; McBride, B. 1994 Ideal Gas Thermodynamic Data for Combustion and Air-Pollution Use; TECHNION-Israel Institute of Technology, Faculty of Aerospace Engineering, Haifa, 1994. (31) Heath, J. R.; Saykally, R. J. J. Chem. Phys., 1991, 94, 3271. (32) Kiefer, J. H.; Kapsalis, S. A.; Al-Alami, M. Z.; Budach, K. A. Combust. Flame 1983, 51, 79-93. (33) Baulch, D. L.; Cobos, C. J.; Cox, R. A.; Frank, P.; Hayman, G.; Just, Th.; Kerr, J. A.; Murrells, T.; Pilling, M. J.; Troe, J.; Walker, R. W.; Warnatz, J. Combust. Flame 1994, 98 (Suppl. 1), 59-79. (34) Baulch, D. L.; Cobos, C. J.; Cox, R. A.; Esser, C.; Frank, P.; Just, Th.; Kerr, J. A.; Pilling, M. J.; Troe, J.; Walker, R. W.; Warn, J. J. Phys. Chem. Ref. Data 1992, 21, 411-429. (35) Dean, A. J.; Hanson, R. K. Int. J. Chem. Kinet. 1992, 24, 517532.
